The permittivity of a material describes the relationship between electric flux density and an applied electric field. Permittivity is a function of frequency and the physical and molecular properties of any material. If a relationship between the material permittivity and a physical property of interest can be established, permittivity measurements can be used to infer the measurement of several attributes of, for example, agricultural and food materials, solvents, pharmaceutical materials. This has been used successfully in the measurement of several attributes of agricultural products such as, for example, the water content of grain (Trabelsi and Nelson, IEEE Trans. On Instrumentation and Measurement, Volume 55 (3), 953-963, 2006; Nelson and Trabelsi, Trans. ASABE, Volume 55 (2), 629-636, May 2012; Kraszewski et al., Meas. Sci. Technol., Volume 8, 857-863, 1990), and the fat content of fish (Kent, Food Control, Volume 1, 47-53, 1990). More recently (Duhamel et al., Proc. IEEE MTT-S Int. Microwave Sym. Dig., Denver, Colo., USDA, 107-110, 1997; Joines et al., Me. Phys., Volume 21, 547-550, April 1994; Trabelsi and Nelson, American Society of Agricultural and Biological Engineers, St. Joseph, Mich., ASABE Paper No. 097305, 2009; Trabelsi and Roelvink, Journal of Microwave Power and Electromagnetic Energy, Volume 48 (4), 215-220, 2014), there has been a focus on using the permittivity of biological materials to identify physical properties such as healthy or diseased human breast tissue (Joines et al., April 1994, supra), or the quality attributes of poultry meat (Trabelsi and Nelson, 2009, supra).
The complex relative permittivity of a material, ε*, is an intrinsic electrical property that relates the electric flux density within the material to an applied electric field. The relative complex permittivity is often written as ε*=ε′−jε″, where ε′ is the dielectric constant and ε″ is the dielectric loss factor. The permittivity (or dielectric properties) is a function of the physical properties of a material, such as the moisture and density of granular and particulate materials. If a relationship between the permittivity and a physical property of interest can be established, permittivity measurements can be used as an indirect, non-destructive method of inferring physical properties. In industrial RF and microwave heating applications, the knowledge of the permittivity of the material to be heated allows rigorous analytical and numerical design of heating cavities and other electromagnetic heating apparatus. The development of sensors and techniques for accurately and efficiently measuring the permittivity of agricultural and biological materials is therefore an area of research with significant commercial potential.
Relationships between the physical and dielectric properties of materials have been reported in several previous studies. Examples for agricultural products are sensors for measuring the water content of grain (Nelson and Trabelsi, ASABE, Volume 55(2), 629-636, 2012), or the fat content of fish (Kent, Food Control, Volume 1, 47-53, 1990). Examples for biological materials are methods for inferring quality attributes of poultry meat (Trabelsi and Nelson, ASABE Paper No. 097305, American Society of Agricultural and Biological Engineers, 2009) or differences between normal and diseased human breast tissue (Joines et al., 1994, supra). The permittivity of biological tissue such as poultry meat depends on a number of factors related to the quality parameters, such as water holding capacity and pH (Trabelsi and Nelson, 2009, supra; Trabelsi, American Society of Agricultural and Biological Engineers, 2012, ASABE Paper No. 121337363). Such properties can vary over a given sample volume, thus the permittivity of poultry meat is often heterogeneous and anisotropic (Clerjon and Damez, Meas. Sci. Technol., Volume 18, 1038-1045, 2007). The degree of anisotropy is a parameter that can be used to estimate parameters such as tissue age (Damez et al, Journal of Food Engineering, Volume 85, 116-122, 2008) or the difference between fresh and frozen meat (Clerjon and Damez, 2007, supra). A convenient measurement method for characterizing dielectric anisotropy of materials would be very useful.
Many techniques have been developed for determining the permittivity of materials (Baker-Jarvis et al., IEEE Trans. Microwave Theory Tech., Volume 38 (8), 1096-1103, August, 1990; Pournaropoulos and Misra, Meas. Sci. Technol., Volume 8 (11), 1191-1202, 1997; Knöchel et al., Meas. Sci. Technol., Volume 18 (4), 1061-1068, 2007; Baker-Jarvis et al., NIST Tech. Note 1536, 2005), some of which have been implemented as industrial sensors (Nyfors and Vainikainen, Industrial Microwave Sensors. Norwood, Mass., USA: Artech House, 1989). Perhaps the most commonly utilized modern method for measuring the permittivity of liquids involves the use of an open-ended coaxial-line probe (Pournaropoulos and Misra, 1997, supra). Its popularity is largely due to relatively simple calibration procedures (Kraszewski et al., IEEE Trans. Instrum. Meas., Volume 32 (2), 385-387, June 1983), its ability to measure over a wide range of frequencies, and its commercial availability (Agilent-Technologies, Agilent 85070E Dielectric Probe Kit: 200 MHz to 50 GHz Technical Overview). However, to measure the permittivity of water-based materials, which have relatively large dielectric constants, the coaxial-line probe must be relatively small to avoid radiation effects (Wei and Sridhar, Proc. IEEE MTT-S Int. Microwave Symp. Dig., Albuquerque, N. Mex., USA, 1271-1274, 1992; Wei and Sridhar, IEEE Trans. Microwave Theory Tech., Volume 39 (3), 526-531, March 1991). Therefore, for biological materials, only a small volume of material can be measured (Hagl et al., IEEE Trans. Microwave Theory Tech., Volume 51 (4), 1194-1206, April 2003). In addition, the open-ended coaxial-line probe cannot be conveniently used to characterize the dielectric anisotropy of materials, (Clerjon and Damez, Meas. Sci. Technol., Volume 18, 1038-1045, 2007).
Transmission lines are often used to measure the broad-band complex permittivity of liquid and semisolid materials (Baker-Jarvis et al., IEEE Trans. Microwave Theory Tech., Volume 38, 1096-1103, 1990). The measurement is typically made by placing the material in a section of transmission line and measuring the two-port complex scattering parameters over a range of frequencies. The complex line propagation constant, γ, can be obtained from the scattering parameters by various methods. The complex relative permittivity of the material can then be found from a model that relates ε* to γ. This model is dependent on the transmission-line dimensions and type, e.g., waveguide, coaxial line, planar line. Compared to the open-ended coaxial-line probe, these transmission line arrangements offer the advantage of measuring the average permittivity of the material along the length of line. The sensing length, and therefore the material volume, can be large relative to volumes sensed by open-ended coaxial-line probes. However, the closed structures of many of these transmission line types, (e.g., waveguide and coaxial line) mean that considerable sample preparation is necessary. Closed transmission lines cannot be conveniently used to measure the permittivity of materials outside a laboratory.
Planar transmission lines, such as coplanar waveguide (CPW), can be configured as permittivity sensors (Stuchly and Bassey, Meas. Sci. Technol., Volume 9, 1324-1329, 1998). The open structure of these transmission lines requires relatively less sample preparation compared to closed transmission-line types because the sample material can be easily placed in contact with the lines without needing to mechanically connect a section of sample-filled transmission line. To numerically extract ε* from γ, either closed-form approximations for the CPW parameters (Roelvink and Trabelsi, IEEE Trans. Instr. Meas., Volume 62 (11), 2974-2982, 2013; herein incorporated by reference in its entirety) or full-wave numerical techniques can be applied (Huynen et al., IEEE Trans. Microwave Theory Tech., Volume 42 (11), 2099-2106, 1994). However, a significant limitation of these approaches is that neither allows ε* to be directly calculated from γ, and numerical iterative methods must be used. Moreover, it has been demonstrated for planar line parameters (Roelvink and Trabelsi, IEEE Trans. Instr. Meas., 2013, supra), that the ε* extracted from such an approach is very sensitive to the line dimensions, particularly for materials with relatively large dielectric constants, such as water-based biological materials. A small uncertainty in these dimensions can result in considerable uncertainty in the measured ε*. If the planar lines are fabricated with low-cost equipment, the dimensional uncertainty is often large. For such situations an alternative approach such as a calibration procedure for extracting ε* that does not required a precise knowledge of the line dimensions would be very useful.
Existing methods for measuring the permittivity tensor of materials with anisotropic dielectric properties generally operate by placing a sample in a section of waveguide or coaxial transmission line and measuring the two-port scattering parameters with the sample ‘grain’ oriented in two ways; parallel and perpendicular to the transverse electric field component of the propagating wave (Akhtar et al., IEEE Trans. Microwave Theory Tech., Volume 54, 2011-2022, 2006; Torgovnikov, Dielectric Properties of Wood and Wood-Based materials, Wood Science, ed. Timell, 1993, Berlin: Springer-Verlag). These methods require that the sample be carefully prepared and are mechanically time consuming. Moreover, for biological materials such as muscle tissue, it can be difficult to precisely identify the direction of the grain. If the sample is not properly aligned, this approach does not provide an accurate measurement of the permittivity tensor. The high level of precision means that such an approach is not well suited to measurements outside the laboratory.
There have been a number of studies that use planar or strip transmission lines to measure permittivity. Stuchly and Bassey (1998, supra) investigated the use of CPW for measuring ε′. In their study, ε′ was determined by a technique that did not account for the source and load mismatch terms associated with the line or the sample-edge discontinuities. While suitable when ε′ is small, for the larger ε′ of biological materials a different approach is required.
Raj et al. (IEEE Trans. Instrum. Meas., Volume 50 (4), 905-909, August 2001) considered measuring liquids with a multilayered CPW configuration. To calibrate their sensor, as well as accounting for the sample-edge discontinuities, a set of calibration liquids with known ε* was measured, and empirical curve fitting was used. The empirically obtained curves are a function of the CPW dimensions and, therefore, new curves are needed for any change in dimension.
Huynen et al., (IEEE Trans. Instrum. Meas., Volume 50 (5), 1343-1348, October 2001) investigated the use of the multiline (Engen and Hoer, IEEE Trans. Microwave Theory Tech., Volume 27 (12), 897-903, December 1979; Marks, IEEE Trans. Microwave Theory Tech., Volume 39 (7), 1205-1215, July 1991) or line-line (Huynen et al, October 2001, supra) technique to measure the propagation constant of a microstrip line formed on a low-loss laminate substrate material. The multiline technique determines γ by measuring two transmission lines that are identical, apart from a known length difference. This technique is therefore attractive for use with planar transmission lines, because γ can be determined independent of any discontinuities. A numerical analysis (Huynen et al., October 2001, supra), based on a variational formulation (Huynen et al., IEEE Trans. Microwave Theory Tech., Volume 42 (11), 2099-2106, November 1994) was used to extract the substrate permittivity from the measured propagation constant. While the configuration (Huynen et al, October 2001, supra) is suitable for permittivity measurements of substrate materials, it is not mechanically suited to the measurement of materials placed on the planar line because considerable sample preparation is necessary to ensure that the two samples are identical, apart from a known length difference. In addition, the method adopted for the numerical extraction of the material permittivity requires significant computational resources.
The permittivity of a material is a function of its physical properties. Numerous techniques and configurations have been used to measure the permittivity of materials, as described above. For planar transmission-line sensors, there are several ways to extract ε* from the measured γ. One way is to use numerical techniques such as the spectral-domain technique (Huynen et al., 1994, supra) or the “method-of-moments” (Sonnet, www.sonnetsoftware.com). Numerical techniques, however, require considerable computational resources in order to obtain accurate results and therefore they are not particularly suited for rapid permittivity measurements in industrial settings. Another approach is to use analytic models that relate the line dimensions/parameters to γ (Roelvink et al., 2013, supra; Stuchly and Bassey, 1998, supra; Raj et al., August 2001, supra). Such models can provide accurate results if the line dimensions/parameters are known. However, as demonstrated (Roelvink and Trabelsi, 2012 IEEE International Symposium on Antennas and Propagation and USNC-URSI National Radio Science Meeting, Chicago, Ill., 2012; herein incorporated by reference in its entirety), small dimensional uncertainties, particularly in regions where the fields are relatively concentrated, can result in large measurement uncertainty. This uncertainty increases as the dielectric constant C of the material increases (Roelvink and Trabelsi, Symposium and Meeting 2012, supra). If low-cost equipment is used to manufacture the planar transmission-line sensor, the dimensional uncertainty can be large. For such situations, an alternative approach for extracting ε* from γ that does not require a precise knowledge of the line dimensions would be useful.
While various methods have been developed for measurement of properties of different materials, there remains a need in the art for a method for rapid, non-destructive, wideband permittivity measurements of materials such as liquids, powders, and semi-solid materials, especially those without uniform edges. There also remains a need in the art for a simple method for measuring the permittivity of materials with anisotropic properties. There also remains a need in the art for a simple calibration procedure for determining the material permittivity from the propagation constant measured with planar transmission lines. The present invention provides a simple two standard calibration technique and low-cost planar transmission-line sensor apparatus for rapid permittivity measurements on liquid, powders, and semisolid materials, which requires minimal sample preparation. It is also well suited for use in industrial environments as a sensor to determine moisture and density of powdered materials, quality parameters of food products such as meat, powdered foods, foods with a semi-solid consistency, and for characterization of biological materials to determine the physical properties of the material, such as the presence or absence of disease.